Quantum-limited Extreme Ultraviolet Coherent Diffraction Imaging

ABSTRACT

Apparatus and methods for coherent diffraction imaging This is accomplished by acquiring data in a CDI setup with a CMOS or similar detector. The object is illuminated with coherent light such as EUV light which may be pulsed. This generates diffraction patterns which are collected by the detector, either in frames or continuously (by recording the scan position during collection). Pixels in the CDI data are thresholded and set to zero photons if the pixel is below the threshold level. Pixels above the threshold may be set to a value indicating one photon, or multiple thresholds may be used to set pixels values to one photon, two photons, etc. In addition, multiple threshold values may be used to detect different photon energies for illumination at multiple wavelengths.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to coherent diffraction imaging. Inparticular, the present invention relates to quantum-limited extendedultraviolet (including x-ray) coherent diffraction imaging.

Discussion of Related Art

Recent work demonstrating imaging using coherent light at 13.5 nmwavelength has yielded the highest-resolution full-field optical imagingas-yet demonstrated in a tabletop-scale setup. A resolution of 12.6 nmhas been achieved using Coherent Diffractive Imaging (CDI), whichdirectly detects the light scattered from an object without the use ofan imaging optics, then reconstructs an image computationally. CDItechniques have had an outsize impact on extended-ultraviolet (EUV) andx-ray imaging, because prior to CDI, imaging resolution was severelylimited by limitations in the imaging optics, which were only capable of˜5-10× the diffraction limit.

By eliminating all optics between the object and the detector, andreplacing them with a computational algorithm, it is possible toimplement high-numerical aperture (NA), diffraction-limited phaseimaging for the first time in this wavelength region. Combined with theuse of very short wavelengths, the result is a new nanoimaging techniquethat can provide fundamentally new nanoimaging capabilities, such aselemental sensitivity and the ability to stroboscopically image dynamicsand function. Furthermore, in CDI, virtually every photon scattered froman object can be detected by the imaging detector, making it the mostphoton efficient form of imaging. Again, for x-ray imaging, dose on thesample is often a critical limitation, particularly for imaging ofliving systems. Conventional x-ray microscopy quickly kills any sampledue to ionizing radiation exposure.

However, one serious limitation of CDI techniques is the limited readoutrate of the EUV sensitive charge-coupled device (CCD) detectors.Ptychographic CDI scans the illumination over a sample, takingdozens-to-thousands of individual diffraction images to recover a singlereconstructed image. In practice using commercially-available EUVsensitive CCD's, the readout rate is limited to <1 fps. Furthermore,since exposure times to saturate the detector are often <<1 sec, imagingis slow and most of the photon flux from the source is wasted—since thebeam is blocked during imager readout.

Virtually all consumer, as well as many scientific imaging applications,have shifted to the use of complementary metal-oxide-semiconductor(CMOS), rather than CCD detectors. Although the fundamental sensitivitymechanism—photon absorption in silicon—is identical between the twotypes of imagers, in the CMOS imager, a charge-to-voltage conversion isdone at each pixel. CMOS imagers use standard fabrication technologies,and are much more amenable to parallel readout, making high frame ratesmuch easier to achieve. Furthermore, more-recently CMOS has exceeded thesignal-to-noise (S/N) levels of CCDs, because the signals are amplifiedin the pixel before leaving the chip. State-of-the-art CMOS detectorshave an S/N level of ˜2 electrons RMS, and specialized readouts or pixelstructures can allow for sub-electron noise; i.e. photoelectroncounting. The remaining disadvantage of the CMOS detector—fixed patternnoise due to fluctuations in amplifier gain—has been mitigated byroutine pixel-by-pixel calibration and background subtraction.

This mode of operation is important for CDI imaging. The typical CDIdiffraction pattern exhibits a very high dynamic range (HDR), muchlarger than in conventional imaging. In general, CDI images distributedata on the image in “Fourier space”, so that fine details correspond tophotons scattered at large angles with respect to the speculardirection, while large features scatter to small angles.

The extreme example of this is in imaging a completely flat, featurelesssurface; i.e. a mirror. In this case, the incident illumination isspecularly reflected, with all the signal hitting a small region nearthe center of the detector, with no signal away from the specularregion. In contrast, in “real space” imaging using optics to convert thescattered light back into an image, the image would be uniform over theentire surface.

Unfortunately, CMOS technology has not yet been commercialized forimaging in the deep-ultraviolet to x-ray regions of the spectrum. UsingCMOS imaging detectors to detect photons in the EUV spectral range,however, does not present any unique challenges—it is technicallyfeasible and simply requires an appropriate imager design. Theavailability of high-speed CMOS detectors (also called CMOS active pixeldetectors) for EUV, furthermore has significant potential to allow for anew regime of high-speed quantum-limited CDI.

A need remains in the art for quantum-limited extended ultravioletcoherent diffraction imaging.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide apparatus andmethods for coherent diffraction imaging in the extended ultraviolet tosoft x-ray range. This is accomplished by acquiring data in a CDI setupwith a CMOS or similar detector. A method of coherent diffractionimaging (CDI) of an object is accomplished by first collecting raw data,by illuminating the object with coherent light (for example extended UVor soft x-ray light), measuring diffraction patterns from the object(from reflection, transmission, or a combination) with a detector suchas a CMOS active pixel detector, and generating raw CDI data. Next, theraw CDI data pixels are thresholded. Pixels below a threshold areconsidered to have detected no photons, while pixels above the thresholdare considered to have detected on photon. Another higher threshold maybe added, between the two thresholds are considered to have detected onpixels and pixels above the higher threshold are considered to havedetected two pixels. and so on.

Generally, some preprocessing is done with the raw CDI data, beforethresholding and/or after. This could include background subtraction,antiblooming, removing readout noise, removing bad pixels, and removingcosmic gamma rays, etc. Finally, after thresholding and preprocessing,the CDI data is reconstructed into an image of the object. Thereconstruction algorithm might include Poisson denoising.

Generally, the illumination is scanned with respect to the object, bymoving the object, the illumination beam, or both. Diffraction patternsare collected during the scanning process. The scanning may stop andstart, with data collected while scanning is stopped. A usefulembodiment collects many frames of data at each stopping point and addsthem together for better accuracy—it is preferable to threshold thepixels before doing this so noise doesn't add up. Alternatively, whenthe illumination beam is pulsed, it is possible to scan continuously,without stopping. In this case the scanning location is recorded overtime, so the imagery accounts for illumination position whenreconstruction is done.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram showing the overall process of quantum-limitedextended ultraviolet coherent diffraction imaging according to thepresent invention.

FIGS. 2A and 2B are flow diagrams showing examples of the dataacquisition step of FIG. 1 in more detail.

FIGS. 2C and 2D are diagrams illustrating the physical process of FIGS.2A and 2B respectively.

FIG. 3 is a flow diagram illustrating an example of the thresholdingstep of FIG. 1 in more detail.

FIG. 4 is a flow diagram illustrating an example of the datapreprocessing step of FIG. 1 in more detail.

FIG. 5 is a diagram illustrating an antiblooming algorithm which mayoptionally be performed as part of the data preprocessing step of FIG.1.

FIG. 6 is a block diagram illustrating a first CDI data acquisitionconfiguration according to the present invention.

FIG. 7 is a block diagram illustrating a second CDI data acquisitionconfiguration according to the present invention.

FIG. 8 is a block diagram illustrating a third CDI data acquisitionconfiguration according to the present invention.

FIG. 9 is a block diagram illustrating a fourth CDI data acquisitionconfiguration according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a flow diagram showing the overall process of quantum-limitedextended ultraviolet coherent diffraction imaging according to thepresent invention. In step 101 data is acquired in a CDI configuration(see FIGS. 2A-D). In step 102, detector pixels are thresholded (see FIG.3). In step 103, data preprocessing is performed (see FIG. 4). In step104, the image is reconstructed. FIGS. 6-9 illustrate examples of dataacquisition apparatus. Extended ultraviolet range has a wavelength ofabout 10 nm-200 nm or 10 nm-250 nm, while soft x-ray has a wavelength ofabout 1 nm-10 nm. Extended ultraviolet range includes extreme UV,generally defined as 10 nm-100 nm.

Various modalities of scanning and data acquisition may be performed instep 101. See FIGS. 2A-2D for examples of scanning and data acquisitionmodalities.

Thresholding of detector 615 pixels is performed in step 102. FIG. 3illustrates an example of this process. A typical use of EUV imagingwould be to detect small defects in an object 613 that would otherwisebe invisible to conventional visible or EUV-wavelength imaging due totheir small size. This small size of such a defect means that in CDIimaging, this would correspond to a small number of photons scatteredfar from the specular direction. At high scattering NA, the photonnumbers are small and the detector area is large, while at smallscattering angles many photons are scattered into a small region.

Overall, reliable detection of single photons in the “sparse” region ofthe diffraction data 614 is particularly important for applications suchas detecting small defects, and ultrahigh-resolution imaging. In fact,it is well known that in “Fourier imaging”, spatial filtering, i.e.actually blocking sections of the detector that correspond to largefeatures (i.e. near the center, specular region of the typicaldiffraction pattern) can result in edge enhancement, and enhancement ofsmall features such as defects. The concept of “noiseless” detection ofsingle photons, in particular in reference to single channel detectorssuch as photomultipliers, is well established. The concept here is notthat noise does not correspond to probabilistic statistics in thedetection of photons—this is inherent to the quantum physics. However,the statistical variation in the detection process, at a single-photonlevel—can be eliminated by threshold detection of these single photons.A photomultiplier tube is considered a noiseless detector for singlephoton events, as signal that exceeds threshold is considered a photondetection. Here we extend this concept to the regions of the CMOS activepixel detector where each pixel see <<1 to several photons per exposure,on average.

Here, this concept is brought to CDI imaging (including ptychography) ina way that is specifically suited for use with high repetition-rate EUVsources 603 such as those implemented through high-order harmonicgeneration 602 of a (pulsed) femtosecond laser system beam 601. Atypical number of photons (˜50,000, which can vary due to statistics orsource fluctuations) would be detected on a pixel array 615 for a single“pulse” of the source; i.e. all ˜50,000 photons would arrive at thepixel array essentially simultaneously. In this regime, which isphoton-limited for large scattering angles, there is a new, useful, andefficient mode of operation. Saturation of the detector would be avoidedsince the “brightest” pixel sees at most 100 photons, or a few thousandphotoelectrons, which is well-within the dynamic range capability of atypical 10-14 bit CMOS detector ND converter. On the other hand, at highscattering angle, the data would be acquired in a “noiseless” photoncounting mode, with digitization such that the majority of pixels willsee no signal and will be thresholded to zero photons. Multipleindividual frames at the same scan position can then accumulate withoutadding to statistical noise in the high scattering-angle pixels, andallowing for continuously accumulating data with a dynamic range limitedonly by exposure time. One very useful embodiment takes a plurality offrames for the same exposure time (e.g. 10 frames up to many thousandsof frames, or more narrowly 100 frames up to many thousands of frames)and thresholds the frames before adding them together. Or alternatively,multiple individual frames taken as the beam is scanned to a newposition with each shot, can be used directly as individual frames in aptychography reconstruction that makes use of all the data to improveimage fidelity.

Preprocessing is performed in step 103. FIG. 3 illustrates an example ofthis process. Setting an intensity threshold for “no photon detected” instep 102 allows one, in the case of a sparse, photon-limited data set,to set most of the image to zero values for a pixel. This in many casesallows for preprocessing to compress data sets using, for instance,compressed sensing (CS) based methods or data compression methods. Notethat portions of preprocessing may also occur before thresholding. Forexample, it is common to apply background subtraction to the data, andthis is preferably performed before thresholding.

Poisson denoising & reconstruction is performed in step 104. With theinherent noisy data in EUV photon counting ptychography, improved datadenoising and ptychographic reconstruction algorithms are useful. Mostof the random and structured noise sources in blind x-ray ptychographycan be removed by a recently proposed advanced denoising algorithm,which is termed Alternating Direction Method of Multipliers Denoisingfor Phase Retrieval (ADP). See Chang et al., “Advanced Denoising forX-ray Ptychography,” Arxiv, 1811.02081 (2018). Based on a forwardscattering model and on a maximum a posteriori estimation combined withthe shift-Poisson method for mixed types of noise, the ADP algorithmadds an additional framewise regularization term to further enhance thedenoising process and improve the image quality. As for theptychographic reconstruction algorithm, an improved reconstructionalgorithm with a built-in noise model is useful such as the one with aninherent Poisson noise model for photon statistics, combined with hybridupdating strategies in the iterative algorithms which include both theOrdered Subset (namely, ptychographical iterative engine (PIE) algorithmfamily), and the Scaled Gradient optimization strategies. Possiblestrategies for denoising would be to use photon detection density overregions of the diffraction data that are sparse to estimate localaveraged intensity; i.e. convert imager counts to discrete photons, andthen to convert photons back into a more distributed intensitydistribution. These statistical averaging methods can replace theoriginal data, or be used in conjunction with the original data, andaveraging over regions can be done for amplitude and/or phase data as ismost effective.

To-date, reconstruction algorithms for CDI generally assume a continuousintensity distribution in the data. However, consider a hypotheticalcomparison of a CDI microscope vs a conventional microscope with animaging lens, in the photon-limited regime. In the real world, both theNA and the efficiency of the lens would result in a loss in signal leveland resolution; however, let us assume a perfect, lossless lens. In thiscase, each photon detected in the CDI imaging mode would also bedetected in the conventional imaging mode. Computationally, we can tracethe path of this single photon, to remap from the image plane to thediffraction plane on a photon-by-photon basis.

To accomplish this, one still requires phase retrieval in thereconstruction; however, this concept yields a novel approach, where thereconstruction seeks to solve for a continuous optical phase, but aphoton-by-photon intensity distribution.

FIGS. 2A and 2B are flow diagrams showing examples of the dataacquisition step of FIG. 1 in more detail. FIGS. 2C and 2D are diagramsillustrating the physical process of FIGS. 2A and 2B respectively.

Image acquisition can be accomplished in a number of ways. One couldaccumulate data over a number of exposure pulses to bring the brightestpixels to near their saturation value as shown in FIGS. 2A and 2C. InFIG. 2A, after accumulation of a single frame, the pixel array data areprocessed to identify single photons. More than one frame can then beaccumulated at a given scan position, with photon counts accumulatingas-such in sparse regions, and intensity accumulating as more of a“continuous variable” (though it might still be expressed in mean#photons) to obtain higher dynamic range.

Or, one could accumulate data on a single-shot basis as shown in FIG. 2Band 2D. The latter is particularly attractive for use with ahigh-harmonic generation light source. The driving laser typicallyoperates at a repetition rate in the range of 1 kHz to >10 kHz. This ismuch faster than the readout rate for a CCD detector (typically <1 to ˜4frames per second). However, it is well-matched to the pixel readoutrate for CMOS detectors, which has been demonstrated to many thousandsfps full array readout rates. When used for shot-by-shot dataacquisition, this provides a significant advantage that, inptychographic CDI, the illumination is scanned over the surface toobtain data at a range of overlapping illumination positions. In currentexperiments, this requires moving the illumination to a specificposition on the surface (either by moving the illumination, or by movingthe actual object), stopping, accumulating data, and then moving to anew position. This further slows the acquisition because of themechanics of this motion. On the other hand, for shot-by-shot frameacquisition, this makes it possible to continuously scan theillumination, recording the position of the beam on a shot-by-shotbasis, and pausing data acquisition at-most for short times at the endof a row to raster-scan the image. Although the illustration shows acontinuous motion only in one dimension, this can be extended totwo-dimensional motion paths (for example, a Lissajous pattern scanning,or a spiral motion). Note that other work has proposed a software fixfor continuous scanning with a quasi-continuous source; this modalityhas intrinsic limits that our approach does not. See Helfenstein et al.,“Scanning coherent diffractive imaging methods for actinic extremeultraviolet mask metrology,” Journal of Micro-Nanolithography Mems andMoems 15 (3), 5 (2016).

FIGS. 2C and 2D illustrate the difference between stop-start scanning(FIG. 2C) and continuous scanning (FIG. 2D). Note that the “raster”pattern illustrated here is an over-simplification—often in CDInon-regular scanning modes (ex. Fermat spiral, irregular spacing, etc.)are used to avoid reconstruction artifacts. In FIG. 2C motion of thesample with respect to the beam stops during acquisition, data areaccumulated, and then the sample is moved to a new location.

FIG. 2D shows continuous scanning. For use with light sources that arepulsed at repetition-rates where single-shot frame readout is possible,the position of illumination is moved continuously, and the approximateposition of the acquisition is recorded at the instant when the pulse ofEUV arrives. This allows for fast, continuous scanning and acquisition.The result is a densely-spaced data set, which in its extreme acquiresframes at a positional spacing comparable to, or exceeding, the spatialresolution even when the illumination beam is much larger than this.

FIG. 3 is a flow diagram illustrating an example of thresholding step102 of FIG. 1 in more detail. In the case of widely-used silicon-baseddetectors, an EUV (detectable) photoelectron is created for every ˜4 eVof deposited photon energy. At 13.5 nm wavelength—92 eV photonenergy—about 23 photoelectrons will be generated for each detectedphoton. With achievable readout noise levels of ˜2 photoelectrons orless, it is possible to identify single photons absorbed by a detectorpixel with high reliability, while at higher exposure levels the pixelcount is less precise and forms a “continuous (though obviously stilldigitized) intensity measurement. Single photon sensitive detection, andin particular the ability to reliably identify pixels that did notabsorb a photon allows for digital signal accumulation.

The physics of EUV light absorption in silicon detectors—including bothCCD and CMOS imagers—is well known and characterized. For an uncoated,back-thinned device suitable for EUV, photoabsorption is followed by asecondary electron cascade that yields an average of one generatedphoto-electron for each ˜4 eV of deposited energy. Thus, for EUV imagingusing 92 eV/13.5 nm wavelength light, each absorbed photon generates˜23±5 electrons assuming sqrt(N) Poisson statistics, where N is thegenerated electron number. Since the readout noise of a single pixel is˜2 electrons, the readout fluctuation is dominated by the secondaryelectron multiplication process. This will allow for some degree of“photon counting” in the case of EUV imaging. In-fact, for an incidentphoton number of <<23 photoelectrons on a single pixel, a CMOS detectorcan serve to noiselessly count photons. In the case of using such adetector with visible light (wavelength 400-700 nm, photon energy ˜2-3eV), each incident photon can generate only a single photoelectron in adetector pixel, and single photon counting is not possible with currentcommercial CMOS detector noise levels. The development of visiblephoton-counting “quanta image sensors” can allow this concept to applymore broadly, and in fact the deterministic nature of photon detectionin this case can present a distinct advantage. On the other hand, whenused with EUV light as in the present invention, one or more thresholdvalues can be used, against which the pixel analog-to-digital (ND)conversion value is compared to determine whether 0, 1, or 2 photons,etc., were absorbed in this pixel. For higher exposure levels, thestatistical variations make the photon counts less precise. However, thetechnology exists to reliably resolve the number of photons incident ona pixel when the number is low, while also allowing for the accumulationof more “continuously” varying intensity information at higher exposurelevels. The simplest manifestation of such a quantization would be todivide the pixel value by the mean number of photoelectrons per EUVphoton (determined experimentally from regions where isolated singlephotons are detected) and then to do an integer rounding. Note that thethreshold may be set to different levels for different pixels or indifferent areas of the detector, for example if the detector sensitivityvaries. However, more sophisticated algorithms that set the thresholdsfor small photon numbers, or that look at neighboring pixels in thephoton sparse regions to take into account blooming, are useful in somecases (see FIG. 5). These algorithms can be implemented in software, butalso amenable to direct FPGA hardware implementation or GPUs. The dataacquisition and reconstruction may be concurrent; i.e. reconstructioncan build in accuracy as data sets are added; or sub-regions can bereconstructed as data acquisition continues to scan new regions of theobject.

In the simplest manifestation, this thresholding could correspond to 1)background subtraction on each pixel; 2) dividing the pixel value by theexpected number of photoelectrons for the illumination wavelength (whichcan take into account the individual pixel gain), and 3) rounding to thenearest integer. Antiblooming algorithms and more-sophisticatedthresholding all would add further refinement.

FIG. 4 is a flow diagram illustrating an example of data preprocessingstep 103 of FIG. 1 in more detail. Setting an intensity threshold for“no photon detected” allows one, in the case of a sparse, photon-limiteddata set, to set most of the image to zero values for a pixel. This inmany cases allows for preprocessing to compress data sets using, forinstance, compressed sensing (CS) based methods. For example, in thecase of a small number of photons detected per frame, the locations ofall the nonzero pixels can be read out, skipping the zero pixels. Inanother case where some pixels may detect more than one photon, thesedata might also include the pixel intensity/photon number. Other readoutoptions might resemble more of a “data compression” approach, which aseries of zero-valued pixels with a zero-run-length code. In any case,since data transfer from the imager 615 will be a performance limitingstep due to transfer rates and energy usage, these modes may all play arole, and the system can be adaptive to a variety of environments; i.e.automatically choose the most appropriate data transfer mode. This dataprocessing can be done using FPGA's, GPUs, or more-conventionalimplementations.

As for the CS methods, one can implement it not only on theoptical/EUV/x-ray domain but also on the electronic domain, enabled bythe recent advances in CMOS sensor technology to implement smart imagingdevice with the possibility of on-chip data (pre)processing for CDI.Note that in addition to high speed data preprocessing and acquisition,CS has been used to overcome reconstruction artifacts in CDI due tomissing data in the diffraction pattern, and to reach the subwavelengthspatial resolution if the sample is sparse in a known basis such ascircles on a grid. Machine learning methods are also now being used forCDI image reconstruction.

FIG. 5 is a diagram illustrating an antiblooming algorithm which mayoptionally be performed as part of the data preprocessing step 103 ofFIG. 1. This would generally be performed before the thresholding step.Another question that can be an issue with EUV imaging is the case ofblooming of single photon events, where the photon is absorbed at apixel boundary or corner. With a sufficiently high S/N, the readoutvalues of adjacent pixels can be summed together to determine whethersuch an event might be part of the readout data. Since this type ofblooming is a uniform-probability event, blooming may also simplycontribute to a decreased quantum efficiency of photon detection. Incases of good photon statistics, the position of the detected photon maybe determined with sub-pixel accuracy by an interpolation-based imageenhancement technique to determine image centroids.

FIG. 5 shows an isolated region of pixels, with pixel #5 identified asthe local maximum. Surrounding pixels that have a photon number readoutexceeding a noise threshold might comprise pixels 6, 8, and 9. Aweighting of the intensities of these pixels, or fitting of a Gaussiancurve can provide sub-pixel spatial resolution (denoted by centroid C).Additionally, the total pixel intensities can be summed to determine thenumber of photons in this region in case of >1. Fitting to adistribution function is also possible for centroiding. Similarprocedures are used for identifying centroid events in direct electrondetection in electron microscopes, but have not been to our knowledgeemployed for photons in the EUV, for imaging. These algorithms can beimplemented in software or hardware (i.e. FPGA's).

FIGS. 6-9 are a block diagrams illustrating CDI data acquisitionconfigurations. FIG. 6 shows a driving laser pulse 601 entering an HHGelement 602. 603 is a beam containing the EUV or X-ray beam generated byHHG element 602, along with remaining driving laser light. The remainingdriving laser light is preferably removed by rejecting mirrors 604, 605and filter 607 (e.g. multiple thin metal filters). This prevents damageto optical elements and other complications. Wavelength selecting mirror609 reflects a single wavelength, as illumination beam 612 must becoherent and ellipsoidal mirror 611 would reflect broadband light. Thus,object illumination beam 612 comprises a single wavelength EUV/x-raybeam. Object 613 (or alternatively beam 612) is scanned (see FIGS.2A-D). Object illumination beam 612 is reflected off of object 613, andthe resulting reflected diffraction pattern 614 is detected by detector615. The configuration of FIG. 7 is similar, but illumination beam 612is transmitted through object 613. A combination of reflection andtransmission is also possible.

FIGS. 8 and 9 use flat/spherical mirror pair 809, 811 in place ofwavelength selecting mirror 609 in order to select a single wavelength.FIG. 8 shows a reflection mode device while FIG. 9 shows a transmissionmode device. Again, these could be combined.

Quantum-Limited Hyperspectral Imaging

The secondary electron generation process that occurs when the detector615 absorbs a high-energy photon can also be used to determine theenergy of the absorbed photon through the total number of detectedphotons. This can be used for hyperspectral CDI imaging. Generally, thepixel readout noise in determining the energy of the incident photon islow compared with the statistical fluctuation in the secondary electronprocess. In the case where the photoelectron number statistics arePoisson (which may or may not be the case depending on the dynamics),the fractional energy or bandwidth resolution would relate toΔλ/λ=ΔE/E˜1/√{square root over (E_(ph)/E_(se))} where E_(ph) is thephoton energy, while E_(se) is the average energy needed to generate asecondary electron; i.e. ˜4 eV for silicon. The energy resolutionrequirement for CDI imaging depends on a number of factors including thetarget resolution and illumination spot size. However, generally it hasbeen found that a fractional bandwidth ΔE/E˜10% can be used effectivelyin a quasi-monochromatic ptychographic reconstruction. In a special casewhere a polychromatic or broadband ptychographic reconstructionalgorithm is utilized, the fractional bandwidth can be extended toΔE/E˜30% or more, at the cost of reduced spatial resolution due to imageblur. This resolution could be obtained in the case of the “waterwindow” soft x-ray imaging, with E_(ph)˜300-500 eV. Future photondetectors such as superconducting transition edge sensor arrays canallow for much higher (˜1 eV demonstrated in single-pixel TE sensors)energy resolution.

This mode of operation is especially helpful for soft x-ray microscopyusing high harmonic sources. By driving the high harmonic process withmid-infrared lasers, λ≥1.5 μm in wavelength, coherent light in this softx-ray spectral region can be generated. However, the light emerges as abroadband spectral continuum, and spectral filtering and focusing ofthis light are very inefficient processes in the soft x-ray region.Normal incidence multilayer reflectors generally have low 10%reflectivity, as well as narrow spectral bandwidth that can be ˜1%,dramatically cutting-down the flux. Grazing incidence monochromators maybe used as an energy filter, but also tend not to be particularlyefficient (˜10%). The ability to use the entire spectrum of emission forillumination generally both increases the available flux and allows fora series of hyperspectral images to be obtained in a single dataacquisition process by energy labeling individual photons detected witha high-speed frame imager. This modality is effective for dataacquisition modes where individual photons are detected by the imagesensor; i.e. low overall flux, or the use of high dynamic range dataacquisition, using both a very low flux mode where the “bright” regionsof the scattered light pattern are imaged, and a maximum flux mode toobtain sensitive acquisition at high NA.

The options for focusing of illumination are also more limiting, andlimited, in the soft x-ray region compared with the EUV. Grazingincidence focusing optics can be used to obtain small focal spot sizeover a broad spectral bandwidth. This can be done either with anellipsoidal (or similar) shape reflector (very expensive,super-precision optical figure, hard to align), or a two- or more-mirrorassembly such as a Kirkpatrick-Baez setup. Both will be limited in spotsize by the fact that grazing incidence focusing necessarily meanslow-NA focusing; i.e. the radius of curvature r_(focus)>>λ. However,this only relates to the illumination and thus is feasible. However,zone plates are more commonly used for focusing in the soft x-rayspectral region, since diffractive optics can be used more successfullyfor relatively tight focusing to r_(focus)˜10λ. In the soft x-rayregion, this does allow for a very tight illumination focus. This willtend to increase the usable spectral bandwidth reconstruction.

However, the zone plate focal length is very chromatic, with focallength f∝λ. Thus, the focal plane of the illumination will depend on thewavelength. For a broadband source, this could be seen as a seriousproblem. However, it may also be used to advantage. The relationshipbetween focal point and wavelength is well defined, so that if thephoton energy or the spectrum of the illumination is known, it can berelated to the size and wavefront of the focal spot illumination (forsamples that are thin compared with the confocal parameter of theillumination) or spot-size vs depth. Furthermore, for imaging in thesoft x-ray region, thresholding is even more effective than it is in theEUV for multi-frame accumulation with low photon number.

What is claimed is:
 1. A method of coherent diffraction imaging (CDI) ofan object comprising the steps of: (a) collecting raw data generated by—(a1) illuminating the object with coherent object illumination light togenerate diffraction patterns, (a2) measuring diffraction patterns fromthe object with a detector array, and (a3) generating raw CDI datarepresenting the object based on the measured diffraction patterns; (b)thresholding the raw CDI data by applying a first threshold toindividual pixels of raw CDI data and setting the data in pixels beneaththe first threshold to zero detected photons; (c) preprocessing the rawCDI data; and (d) reconstructing imagery of the object from thethresholded preprocessed CDI data by running a CDI reconstructionalgorithm.
 2. The method of claim 1 wherein step (a) further includesthe step (a4) of scanning the object with respect to the objectillumination light and detecting diffraction patterns over time.
 3. Themethod of claim 2 wherein: The illumination beam is scanned across theregion to be imaged, and step (a4) includes the steps of stopping thescan, acquiring data, and resuming the scan; wherein step (a2) includesthe step of measuring diffraction patterns while the scan is stopped;and wherein step (a3) includes the step of forming individual frames ofCDI data from the measured diffraction.
 4. The method of claim 3 whereinsteps (a2) and (a3) form two frames of data while the scan is stopped.5. The method of claim 4 wherein steps (a2) and (a3) form a plurality offrames of data while the scan is stopped.
 6. The method of claim 2wherein: step (a1) illuminates the object with pulses of illumination;step (a4) includes the step of continuously scanning one of either theobject or the illumination; and step (a2) includes the step of recordingscanning position while measuring the diffraction patterns.
 7. Themethod of claim 1 wherein step (a1) illuminates the object withillumination having a frequency in the extended ultraviolet range. 8.The method of claim 1 wherein step (a1) illuminates the object withillumination having a frequency in the soft x-ray range.
 9. The methodof claim 1 wherein step (a2) utilizes a CMOS active pixel detector. 10.The method of claim 1 wherein step (b) sets pixels above the firstthreshold to a value indicating a single photon detected at thosepixels.
 11. The method of claim 1 wherein step (b) further sets a secondthreshold, sets pixels between the first threshold and the secondthreshold to a value indicating a single photon detected at thosepixels, and sets pixels above the second threshold to a value indicatingtwo photons detected at those pixels.
 12. The method of claim 1 whereinstep (c) includes the step of performing an antiblooming algorithm onthe raw CDI data before step (b).
 13. The method of claim 1 wherein step(c) includes the steps of removing readout noise, removing bad pixels,and removing cosmic gamma rays from the raw CDI data.
 14. The method ofclaim 1 wherein step (d) includes Poisson denoising.
 15. Apparatus forcoherent diffraction imaging (CDI) of an object comprising: a source ofcoherent light; optics configured to illuminate the object with thecoherent light; a detector configured to measure diffraction patternsfrom the illuminated object and generate raw CDI data; a processorconfigured threshold the raw CDI data by applying a first threshold toindividual pixels of raw CDI data and setting the data in pixels beneaththe first threshold to zero detected photons, to preprocess the raw CDIdata, and to reconstruct imagery of the object from the thresholdedpreprocessed CDI data by running a CDI reconstruction algorithm.
 16. Theapparatus of claim 15, further comprising a scanning mechanism to scanthe coherent illumination over the object in a pattern.
 17. Theapparatus of claim 16 wherein the scanning mechanism is configured tostop and restart scanning, and wherein the processor is furtherconfigured to form a plurality of frames of data while the scanningmechanism is stopped.
 18. The apparatus of claim 16 wherein the scanningmechanism is configured to scan continuously, and wherein the processoris further configured to periodically record scanning positions.
 19. Theapparatus of claim 15 wherein the detector is a CMOS active pixeldetector.
 20. The apparatus of claim 15 wherein the source providesextended UV light.
 21. The apparatus of claim 15 wherein the sourceprovides soft x-ray light.